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Equilibrium conversion for a Pd-based membrane reactor. Dependence on the temperature and pressure
Chemical Engineering and Processing 42 (2003) 231 /236 www.elsevier.com/locate/cep
Equilibrium conversion for a Pd-based membrane reactor. Dependence on the temperature and pressure Giuseppe Marigliano a, Giuseppe Barbieri a,*, Enrico Drioli a,b a
Research Institute on Membrane Technology, ITM-CNR, (former IRMERC-CNR), c/o University of Calabria, via Pietro Bucci, I-87030 Rende (CS), Italy b Department of Chemical Engineering and Materials, University of Calabria, Via Pietro Bucci, I-87030 Rende (CS), Italy Received 9 April 2001; received in revised form 8 June 2001; accepted 1 October 2001
Abstract A thermodynamic tool based on the ‘reactor in series method’ was used to evaluate the equilibrium conversion of dehydrogenation reactions such as methane steam reforming (MSR) and water gas shift (WGS) in a Pd-based membrane reactor (MR). The permeation equilibrium, expressed by the equality of the H2 partial pressure on reaction and permeate sides, was imposed as the further constrain for MR. The equilibrium conversion shift is an increasing function of the sweep factor, which is an index of the extractive capacity of the membrane system. The equilibrium conversion of a MR was analysed as a function of temperature and pressure. It shows the same trend vs. temperature for MR and traditional reactor (TR). On the contrary, pressure play a very important role because it has a different influence on the equilibrium of MR with respect to a TR. In particular, the positive effect on thermodynamic conversion was shown also for the MSR reaction characterised by Dn /0. # 2003 Elsevier Science B.V. All rights reserved. Keywords: Membrane reactor equilibrium; Methane steam reforming; Water gas shift
1. Introduction Developed Countries worked out an energy planetary policy whose objectives are: rational use of energy and environmental safeguard. These Countries, that highly depend on the import of energetic source, also have to take into account the strategic objective of ensuring energy supply by exploiting different energetic sources. The energy /environment connection, which has represented a tendency line, is nowadays becoming the prevailing trend. In particular, the reduction of the green house gases (e.g. CO2 and CH4) emission is considered, in the Kyoto protocol, one of air pollution major problems. The implementation of the Kyoto protocol will have a strong impact on the exploitation of energetic sources and technologies, favouring the sources at lower carbon content and technologies of conversion and final use with higher efficiency. The
* Corresponding author. Tel.: /39-0984-492012; fax: /39-0984402103 E-mail address: [email protected] (G. Barbieri).
chemistry of C1 /C3 and H2 (used both as fuels and as energetic vector, e.g. in the fuel cells) is of growing interest. Membrane technologies, and in particular the membrane reactors (MRs), might have a very important role in the development of new processes with a high energetic efficiency. MRs, coupling reaction and separation, can achieve higher conversion with respect to traditional reactors (TRs), at the same operating conditions, for product selective removal. In the present work, Pd-based membranes, permeable only to H2, will be considered in order to analyse the equilibrium of dehydrogenation reactions (e.g. methane steam reforming (MSR), water gas shift (WGS)) in a MR. Several hydrogenation/dehydrogenation reactions were studied in Pd-based MRs. Oertel et al. [1] studied steam reforming of natural gas for hydrogen production. Shu et al. [2] studied MSR in an isothermal catalytic MR with a Pd /Ag membrane supported on porous stainless steel. MSR was studied [3,4] in catalytic Pd-based MRs in order to analyse the thermal effect on the methane yield.
0255-2701/03/$ - see front matter # 2003 Elsevier Science B.V. All rights reserved. PII: S 0 2 5 5 - 2 7 0 1 ( 0 2 ) 0 0 0 9 2 - 2
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These studies confirmed the MR advantages (e.g. higher conversion) with respect to TRs. Reactor modelling and/or simulations are reported in various papers. A 2-D mathematical model of MR was proposed by Becker et al. [5] in order to study the ethyl benzene dehydrogenation. Hara et al. [6] studied the effect of the selectively separation of H2 on CH3OH decomposition. MSR process was simulated by Oklany et al. [7,8] for a Pd-based MR for co-current flows, whereas, a mathematical model for the same reaction in a MR with counter-current flows was developed by Barbieri and Di Maio [9]. Energy transport through a Pd-based membrane was analysed by Marigliano et al. [10]. The maximum attainable conversion in a porous MR was analysed [11] as a function of different parameters such as Thiele module, permeation characteristic, etc. In the various experimental and modelling/simulation works present in the open literature, however, studies on the MR thermodynamic equilibrium are relatively absent. Barbieri et al. [12] have analysed the existence regions for the MSR in a Pd-based MR and discussed how the MR use improves the overall performance overcoming the thermodynamic limits of the TRs. The existence region is, in the conversion /temperature plane, a closed area delimited by the thermodynamic equilibrium curve and the adiabatic and isothermal reaction paths. All reaction paths, when, e.g. feed flow rate, membrane thickness, overall heat transfer coefficient, etc. are changed fell in this closed region. The dimension of the existence region is an increasing function of the sweep factor (I). Due to the potentiality of the MRs and to their growing interest, it is becoming essential to have tools to define their thermodynamic limits. The conversion of a chemical reactor (of finite dimension) depends on several factors, e.g. the reactor model considered */continuous stirred tank reactor (CSTR), plug flow reactor (PFR), batch reactor*/the thermodynamic variables (e.g. T and P ) and the operating variables (e.g. feed flow rate). TPermeate Side, PPermeate Side, I must be considered, for a MR, in order to analyse its conversion dependence on transport mechanism through the membrane of the permeable species (Sievert’s law) and on the geometric parameters (e.g. membrane area and thickness). The equilibrium of a reacting traditional system is a function only of the thermodynamic variables (e.g. T and P ) and from the reactant molar ratio and it is independent from the reactor model or reaction path. The thermodynamic variables and the sweep factor (I ) characterising the permeate side stream must be added to the previous ones in order to calculate the MR equilibrium conversion. In addition to equilibrium constant, another constraint must be taken into account: the permeation equilibrium, which can be ex-
pressed as the equality of the partial pressures on both membrane sides of the permeable species. Chemical equilibrium is independent from the reaction path, thus MR equilibrium is also independent from permeation rate.
2. Membrane reactor models considered Equilibrium conversion of a TR is calculated taking into account the equilibrium constant of any reaction. For a batch reactor the equilibrium is reached, theoretically, in infinite time. The residence time is the characteristic variable of flow systems (PFR, CSTR); and, theoretically, an infinite residence time is necessary to achieve the equilibrium. An infinite residence time might be approximated by a very large reaction volume or by a very low flow rate. The plug-flow MR will be only referred in the following as flow MR. A batch and a plug-flow MRs were considered in this study in order to calculate the MR equilibrium. The first reactor is characterised by variables evolution in time, and the equilibrium is reached when there is no more variation in time. The plug-flow MR, operating in stationary state, is characterised by space variable profiles, and the equilibrium is reached when no more variation occurs in the profiles. In any case, the permeation equilibrium is given by the equation: PReaction i
Side
PPermeate i
Side
0
(1)
Ö permeable species
This condition is independent from the membrane chemical composition and therefore from the permeation rate. H2 permeation in a Pd-based membrane follows the Sievert’s law; no deviation is present above 300 8C [13], hence, the rate determining step is the H2 diffusion through the Pd bulk. However, the membrane characteristic (e.g. Pd, Pd /Ag, etc.) influences the permeation rate and hence the time (the residence time for the plug-flow MR) necessary to reach the equilibrium, but not the final value reached, which depends on permeative capacity of the system. This property is a function of I that is the characterising variable of a MR system. The sweep factor is an index of extractive capacity of a membrane system and is defined for batch and flow MR in Table 1. Table 1 Sweep factor (I ) definition for batch and flow MRs Batch MR Side nPermeate Inert /I / Reaction Side nCH4 or CO
Flow MR I
/
Permeate Side FInert / Reaction Side FCH 4 or CO
G. Marigliano et al. / Chemical Engineering and Processing 42 (2003) 231 /236
Fig. 1. CH4 conversion profile in a plug-flow MR for the MSR reaction at different feed flow rates. PReaction /PPermeate Side /100 kPa, I/10, T/500 8C, reactant (H2O/CH4) molar ratio/3.
The constraint of Eq. (1) and the bond with the I variable are shown in Fig. 1 and Fig. 2. In fact, the final conversion reached using different flow rates is the same at a set I value (Fig. 1). These profiles were calculated using a simulation program (Barbieri et al. [12]) describing the nonisothermal behaviour of co-current MR (no simulations were performed at temperature lower than 400 8C). This final value is achieved when the partial pressure of H2, the product selectively removed from reaction ambient, is the same on both membrane sides (Fig. 2) as required from Eq. (1). The outlet (equilibrium) value of H2 partial pressure is independent from the membrane thickness, even if, the profiles are very different for the membrane thickness considered (d and 10d). They reach the same final value, even if different reactor length are necessary to reach the equilibrium. Similar differences are showed when other parameters of the permeation rate equation, e.g. the membrane area, or permeation law parameters (e.g. for Pd, Pd /Ag, etc. membranes) are changed. The batch MR consists of one reaction and one permeate chambers separated by a selective membrane.
Fig. 2. H2 partial pressure in a plug-flow MR for the MSR reaction for two different values of membrane thickness (d/7.5 mm). PReaction / PPermeate Side /100 kPa, I/10, T/500 8C, reactant (H2O/CH4) molar ratio/3, Q/Feed CH4/ /200 SCCM.
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Each chamber, in order to operate at a constant pressure, is provided with a piston that can move without friction; consequently, the reaction and permeate side volumes change according to the piston movement. In addition, PReaction can be different from PPermeate Side. During the reaction the chamber volumes change in order to achieve the chemical and permeating equilibria. In the plug-flow MR, there are no moving parts as in batch MR, however, permeation changes flow rates of both reaction and permeate streams. Algorithm used for the equilibrium calculation of a MR [12] integrates the method of the reactor in series, already utilised for the calculation of the chemical equilibrium (in TR), with the constrain expressed by the permeating equilibrium, Eq. (1).
3. Results and discussion MSR and WGS reactions have been considered in this work to calculate the MR equilibrium conversion due to their importance in many industrial processes. In particular, MSR is one of the most important industrial processes for H2 [14] and syngas production. The catalytic process involves several elementary reactions, however, a kinetic study of MSR [15] over Ni-based catalysts shows that the reaction rate might consider the following three global reactions: (1) CH4 H2 OCO3H2 (2) COH2 OCO2 H2 (3) CH4 2H2 OCO2 4H2
DH298 206 kJ mol1 DH298 41 kJ mol1 DH298 165 kJ mol1
However, the reaction (3) can be excluded from the thermodynamic analysis because of linear combination of the first two reactions. The WGS reaction (2) is present in many chemical processes, which involve hydrocarbon transformations, e.g., partial oxidation, reforming, etc. The tool developed by Barbieri et al. [12] was used to calculate the equilibrium conversion for a MR when a reaction (e.g. MSR or WGS) occurs. Equilibrium conversion of MSR is an increasing function of T and I (Fig. 3). The increase in the conversion is higher at intermediate T; whilst at a lower T the conversion difference of a MR and a TR decreases because the permeation effect is very low due to low H2 partial pressure in the reaction chamber. At high T (/ 500 8C), the conversion for I /10 is /90%, a further increase in I shifts the equilibrium to a total conversion. The use of a MR is convenient also for the WGS reaction. The conversion is, in this case, a decreasing function of T (Fig. 4); however, it shows a significant increase when I increases. Major advantages were showed at higher T ; at 400 8C the conversion degree
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Fig. 3. CH4 equilibrium conversion vs. T for MSR reaction at different I values. PReaction /PPermeate Side /1 bar, reactant (H2O/ CH4) molar ratio/3.
Fig. 4. CO equilibrium conversion vs. T for WGS reaction at different I values. PReaction /PPermeate Side /1 bar, reactant (H2O/CO) molar ratio/1.
moves from 75% for a TR to about 90% for a MR (I/ 10). MSR reaction is characterised by Dn /0 and thus it is not favoured by pressure, as shown, for a TR, in Fig. 5.
Fig. 5. CH4 equilibrium conversion vs. T for MSR reaction at different reaction pressures. PPermeate Side /1 bar, reactant (H2O/ CH4) molar ratio/3, I/10.
The curves relative to higher pressures are located under the curves corresponding at atmospheric reaction pressure. The situation is completely different for a MR where an increase of the reaction pressure produces an increase in the driving force for the permeation and then a higher equilibrium conversion. The same positive effect is showed by a MR for the WGS reaction (Fig. 6) that is characterised by Dn /0. However, reaction pressure increases the permeation driving force and consequently there is a large advantage in the global performance of the reactor. The pressure has a positive effect on MR equilibrium for any reaction type (Table 2) also for the reaction characterised by Dn /0 such as, e.g. MSR. In addition, the permeation reduces the reaction volume for a batch MR or the outlet reaction stream of a plug-flow MR. In Fig. 7 the CH4 conversion, in the MSR reaction, is reported versus the reaction pressure. The MR conversion is an increasing function of the pressure at higher I; when the reaction temperature and I are lower (0/ 500 8C, I/1) the conversion profile presents a minimum at a lower value (a few bars) of reaction pressure. TR conversion decreases in the whole pressure range. Equilibrium conversion depends on the pressure for two different factors: one negative, due to the reaction pressure, and one positive, due to an increase of the permeation driving force. At 500 8C and I/1 these two effects are comparable, and they generate a minimum. The two opposite effects on the conversion are equal, for a MR at 600 8C with I /1, and the profile presents a flex point. When the permeation is improved increasing I , the flex point disappears. The conversion after the minimum increases monotonically. In a MR, H2 partial pressures on reaction and permeate sides are equal under equilibrium condition. H2 partial pressure shows the same behaviour of the conversion degree increasing for a MR and decreasing for a TR (Fig. 8). In addition, it decreases when I
Fig. 6. CO equilibrium conversion vs. T for WGS reaction at different reaction pressures. PPermeate Side /1 bar, reactant (H2O/CO) molar ratio /1, I/10.
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Table 2 Pressure effect and variation of the reaction volume or the outlet flow rate on reaction side in batch or plug-flow TR and MR Mole number variation
Dn B 0 Dn 0 Dn 0
TR
MR
Pressure effect
Batch / Reaction volume variation
Positive No Negative
Reduction No Expansion
Plug-flow / Reaction stream variation
Pressure effect
Batch / Reaction volume variation
Positive Positive Positive
Reduction Reduction Depend on the reaction
Plug-flow / Reaction stream variation
4. Conclusions
Fig. 7. CH4 equilibrium conversion vs. PReaction for MSR reaction. Reactant (H2O/CH4) molar ratio/3.
Fig. 8. H2 partial pressure under equilibrium condition in the MSR reaction. TReaction /500 8C, PReaction /1 bar, reactant (H2O/CH4) molar ratio/3.
Equilibrium conversion of a Pd-based MR was studied for hydrogenation reactions such as MSR and WGS using a thermodynamic tool based on ‘reactor in series method’. In order to evaluate the MR conversion, the relation of the permeating equilibrium was added, as constrain, to the thermodynamic constants already used to calculate the equilibrium of a TR. The equilibrium conversion increase is related to the extractive capacity of the system represented by the sweep factor. Sweep factor is identified, in addition to those characterising a TR, as a characterising variable for a MR. In fact, equilibrium conversion is an increasing function of I. In order to validate the choice of the sweep factor as characterising variable some simulations (using a mathematical model [12]) were performed changing some parameters, e.g. feed and sweep flow rates, membrane thickness, etc. All simulations showed the same result, the same values of equilibrium conversion, at a set I value. The different effect of the reaction pressure on the equilibrium of MRs and TRs is another interesting thermodynamic result. The conversion of a reaction characterised by no variation of the number of moles, e.g. WGS, in a TR is independent from reaction pressure. On the contrary, the conversion is an increasing function of reaction pressure in a MR. This advantage is more evident for the MSR reaction characterised by an increase in the number of moles: a reaction pressure increase gives, in a MR, a higher equilibrium conversion, when in a TR the effect is a strong reduction of conversion.
Acknowledgements increases, whereas, the CH4 conversion and H2 amount increase. Its increase is higher at lower I : at 500 8C, it passes from about 0.3 bar to about 0.75 bar when I decreases from 10 to 1. An analogous behaviour is showed at 600 8C.
The financial contribution of the INCO-Copernicus project Contract No. IC15-CT98 0512 and MURSTItaly project ‘Nuove membrane per la realizzazione e lo sviluppo di reattori catalitici a membrana*/Cofinanziamento 1999’ are gratefully acknowledged.
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Appendix A: Nomenclature List of acronyms CSTR continuous stirred tank reactor MR membrane reactor MSR methane steam reforming PFR plug flow reactor SCCM cm3 (TPS)/min TR traditional reactor WGS water gas shift List of symbols d membrane thickness (mm) DH reaction enthalpy (kJ/mol) Dnj variation of the mole number in the reaction jth I sweep factor, see Table 1 n mole number P pressure (Pa) T temperature (8C) X CH4 or CO conversion
References [1] M. Oertel, J. Schmitz, W. Weirich, D. Jendryseek-Neumann, R. Schulten, Steam reforming of natural gas with integrated hydrogen separation for hydrogen production, Chem. Eng. Tech. 10 (1987) 248 /255. [2] J. Shu, B.P.A. Grandjean, S. Kaliaguine, Methane steam reforming in asymmetric Pd- and Pd /Ag/Porous SS membrane reactor, Appl. Catal. A 119 (1994) 305 /325.
[3] G. Barbieri, V. Violante, F.P. Di Maio, A. Criscuoli, E. Drioli, Methane steam reforming analysis in a palladium-based catalytic membrane reactor, Ind. Eng. Chem. Res. 36 (1997) 3369 /3374. [4] G.S. Madia, G. Barbieri, E. Drioli, Theoretical and experimental analysis of methane steam reforming in a membrane reactor, Can. J. Chem. Eng. 77 (1999) 698 /706. [5] Y.L. Becker, A.G. Dixon, W.R. Moser, Y.H. Ma, Modelling of ethylbenzene dehydrogenation in a catalytic membrane reactor, J. Mem. Sci. 77 (1993) 233 /244. [6] S. Hara, W.-C. Xu, K. Sakaki, N. Itoh, Kinetics and hydrogen removal effect for methanol decomposition, Ind. Eng. Chem. Res. 38 (1999) 488 /492. [7] J.S. Oklany, K. Hou, R. Hughes, A simulative comparison of dense microporous membrane reactors for the steam reforming of methane, Appl. Catal. A 170 (1) (1998) 13 /22. [8] J.S. Oklany, E. Gobina, R. Hughes, A Comparison of the Performance of Catalytic Membrane Reactors for the Process of Steam Reforming, IChem Research Event, University of Leeds, Leeds, UK, 1995. [9] G. Barbieri, F.P. Di Maio, Simulation of the methane steam reforming process in a catalytic Pd-membrane reactor, Ind. Eng. Chem. Res. 36 (6) (1997) 2121 /2127. [10] G. Marigliano, G. Barbieri, E. Drioli, Effect of energy transport on a palladium based membrane reactor for methane steam reforming process, Catal. Today 67/1 (3) (2001) 87 /101. [11] C. Chmielewski, Z. Ziaka, V. Manousiouthakis, Conversion targets for plug flow membrane reactors, Chem. Eng. Sci. 54 (1999) 2979 /2984. [12] G. Barbieri, G. Marigliano, G. Perri, E. Drioli, Conversiontemperature diagram for a palladium membrane reactor. Analysis of an endothermic reaction: methane steam reforming, Ind. Eng. Chem. Res. 40 (2001) 2017 /2026. [13] T.L. Ward, T. Dao, Model of hydrogen permeation behavior in palladium membranes, J. Mem. Sci. 153 (1993) 211 /231. [14] W.H. Scholz, Process for industrial of hydrogen and associated environmental effects, Gas Sep. Purif. 7 (3) (1993) 131 /139. [15] J. Xu, G.F. Froment, Methane steam reforming, methanation and water gas shift: I. Intrinsic kinetics, AIChE J. 35 (1989) 88 /96.
Equilibrium conversion for a Pd-based membrane reactor. Dependence on the temperature and pressure Giuseppe Marigliano a, Giuseppe Barbieri a,*, Enrico Drioli a,b a
Research Institute on Membrane Technology, ITM-CNR, (former IRMERC-CNR), c/o University of Calabria, via Pietro Bucci, I-87030 Rende (CS), Italy b Department of Chemical Engineering and Materials, University of Calabria, Via Pietro Bucci, I-87030 Rende (CS), Italy Received 9 April 2001; received in revised form 8 June 2001; accepted 1 October 2001
Abstract A thermodynamic tool based on the ‘reactor in series method’ was used to evaluate the equilibrium conversion of dehydrogenation reactions such as methane steam reforming (MSR) and water gas shift (WGS) in a Pd-based membrane reactor (MR). The permeation equilibrium, expressed by the equality of the H2 partial pressure on reaction and permeate sides, was imposed as the further constrain for MR. The equilibrium conversion shift is an increasing function of the sweep factor, which is an index of the extractive capacity of the membrane system. The equilibrium conversion of a MR was analysed as a function of temperature and pressure. It shows the same trend vs. temperature for MR and traditional reactor (TR). On the contrary, pressure play a very important role because it has a different influence on the equilibrium of MR with respect to a TR. In particular, the positive effect on thermodynamic conversion was shown also for the MSR reaction characterised by Dn /0. # 2003 Elsevier Science B.V. All rights reserved. Keywords: Membrane reactor equilibrium; Methane steam reforming; Water gas shift
1. Introduction Developed Countries worked out an energy planetary policy whose objectives are: rational use of energy and environmental safeguard. These Countries, that highly depend on the import of energetic source, also have to take into account the strategic objective of ensuring energy supply by exploiting different energetic sources. The energy /environment connection, which has represented a tendency line, is nowadays becoming the prevailing trend. In particular, the reduction of the green house gases (e.g. CO2 and CH4) emission is considered, in the Kyoto protocol, one of air pollution major problems. The implementation of the Kyoto protocol will have a strong impact on the exploitation of energetic sources and technologies, favouring the sources at lower carbon content and technologies of conversion and final use with higher efficiency. The
* Corresponding author. Tel.: /39-0984-492012; fax: /39-0984402103 E-mail address: [email protected] (G. Barbieri).
chemistry of C1 /C3 and H2 (used both as fuels and as energetic vector, e.g. in the fuel cells) is of growing interest. Membrane technologies, and in particular the membrane reactors (MRs), might have a very important role in the development of new processes with a high energetic efficiency. MRs, coupling reaction and separation, can achieve higher conversion with respect to traditional reactors (TRs), at the same operating conditions, for product selective removal. In the present work, Pd-based membranes, permeable only to H2, will be considered in order to analyse the equilibrium of dehydrogenation reactions (e.g. methane steam reforming (MSR), water gas shift (WGS)) in a MR. Several hydrogenation/dehydrogenation reactions were studied in Pd-based MRs. Oertel et al. [1] studied steam reforming of natural gas for hydrogen production. Shu et al. [2] studied MSR in an isothermal catalytic MR with a Pd /Ag membrane supported on porous stainless steel. MSR was studied [3,4] in catalytic Pd-based MRs in order to analyse the thermal effect on the methane yield.
0255-2701/03/$ - see front matter # 2003 Elsevier Science B.V. All rights reserved. PII: S 0 2 5 5 - 2 7 0 1 ( 0 2 ) 0 0 0 9 2 - 2
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These studies confirmed the MR advantages (e.g. higher conversion) with respect to TRs. Reactor modelling and/or simulations are reported in various papers. A 2-D mathematical model of MR was proposed by Becker et al. [5] in order to study the ethyl benzene dehydrogenation. Hara et al. [6] studied the effect of the selectively separation of H2 on CH3OH decomposition. MSR process was simulated by Oklany et al. [7,8] for a Pd-based MR for co-current flows, whereas, a mathematical model for the same reaction in a MR with counter-current flows was developed by Barbieri and Di Maio [9]. Energy transport through a Pd-based membrane was analysed by Marigliano et al. [10]. The maximum attainable conversion in a porous MR was analysed [11] as a function of different parameters such as Thiele module, permeation characteristic, etc. In the various experimental and modelling/simulation works present in the open literature, however, studies on the MR thermodynamic equilibrium are relatively absent. Barbieri et al. [12] have analysed the existence regions for the MSR in a Pd-based MR and discussed how the MR use improves the overall performance overcoming the thermodynamic limits of the TRs. The existence region is, in the conversion /temperature plane, a closed area delimited by the thermodynamic equilibrium curve and the adiabatic and isothermal reaction paths. All reaction paths, when, e.g. feed flow rate, membrane thickness, overall heat transfer coefficient, etc. are changed fell in this closed region. The dimension of the existence region is an increasing function of the sweep factor (I). Due to the potentiality of the MRs and to their growing interest, it is becoming essential to have tools to define their thermodynamic limits. The conversion of a chemical reactor (of finite dimension) depends on several factors, e.g. the reactor model considered */continuous stirred tank reactor (CSTR), plug flow reactor (PFR), batch reactor*/the thermodynamic variables (e.g. T and P ) and the operating variables (e.g. feed flow rate). TPermeate Side, PPermeate Side, I must be considered, for a MR, in order to analyse its conversion dependence on transport mechanism through the membrane of the permeable species (Sievert’s law) and on the geometric parameters (e.g. membrane area and thickness). The equilibrium of a reacting traditional system is a function only of the thermodynamic variables (e.g. T and P ) and from the reactant molar ratio and it is independent from the reactor model or reaction path. The thermodynamic variables and the sweep factor (I ) characterising the permeate side stream must be added to the previous ones in order to calculate the MR equilibrium conversion. In addition to equilibrium constant, another constraint must be taken into account: the permeation equilibrium, which can be ex-
pressed as the equality of the partial pressures on both membrane sides of the permeable species. Chemical equilibrium is independent from the reaction path, thus MR equilibrium is also independent from permeation rate.
2. Membrane reactor models considered Equilibrium conversion of a TR is calculated taking into account the equilibrium constant of any reaction. For a batch reactor the equilibrium is reached, theoretically, in infinite time. The residence time is the characteristic variable of flow systems (PFR, CSTR); and, theoretically, an infinite residence time is necessary to achieve the equilibrium. An infinite residence time might be approximated by a very large reaction volume or by a very low flow rate. The plug-flow MR will be only referred in the following as flow MR. A batch and a plug-flow MRs were considered in this study in order to calculate the MR equilibrium. The first reactor is characterised by variables evolution in time, and the equilibrium is reached when there is no more variation in time. The plug-flow MR, operating in stationary state, is characterised by space variable profiles, and the equilibrium is reached when no more variation occurs in the profiles. In any case, the permeation equilibrium is given by the equation: PReaction i
Side
PPermeate i
Side
0
(1)
Ö permeable species
This condition is independent from the membrane chemical composition and therefore from the permeation rate. H2 permeation in a Pd-based membrane follows the Sievert’s law; no deviation is present above 300 8C [13], hence, the rate determining step is the H2 diffusion through the Pd bulk. However, the membrane characteristic (e.g. Pd, Pd /Ag, etc.) influences the permeation rate and hence the time (the residence time for the plug-flow MR) necessary to reach the equilibrium, but not the final value reached, which depends on permeative capacity of the system. This property is a function of I that is the characterising variable of a MR system. The sweep factor is an index of extractive capacity of a membrane system and is defined for batch and flow MR in Table 1. Table 1 Sweep factor (I ) definition for batch and flow MRs Batch MR Side nPermeate Inert /I / Reaction Side nCH4 or CO
Flow MR I
/
Permeate Side FInert / Reaction Side FCH 4 or CO
G. Marigliano et al. / Chemical Engineering and Processing 42 (2003) 231 /236
Fig. 1. CH4 conversion profile in a plug-flow MR for the MSR reaction at different feed flow rates. PReaction /PPermeate Side /100 kPa, I/10, T/500 8C, reactant (H2O/CH4) molar ratio/3.
The constraint of Eq. (1) and the bond with the I variable are shown in Fig. 1 and Fig. 2. In fact, the final conversion reached using different flow rates is the same at a set I value (Fig. 1). These profiles were calculated using a simulation program (Barbieri et al. [12]) describing the nonisothermal behaviour of co-current MR (no simulations were performed at temperature lower than 400 8C). This final value is achieved when the partial pressure of H2, the product selectively removed from reaction ambient, is the same on both membrane sides (Fig. 2) as required from Eq. (1). The outlet (equilibrium) value of H2 partial pressure is independent from the membrane thickness, even if, the profiles are very different for the membrane thickness considered (d and 10d). They reach the same final value, even if different reactor length are necessary to reach the equilibrium. Similar differences are showed when other parameters of the permeation rate equation, e.g. the membrane area, or permeation law parameters (e.g. for Pd, Pd /Ag, etc. membranes) are changed. The batch MR consists of one reaction and one permeate chambers separated by a selective membrane.
Fig. 2. H2 partial pressure in a plug-flow MR for the MSR reaction for two different values of membrane thickness (d/7.5 mm). PReaction / PPermeate Side /100 kPa, I/10, T/500 8C, reactant (H2O/CH4) molar ratio/3, Q/Feed CH4/ /200 SCCM.
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Each chamber, in order to operate at a constant pressure, is provided with a piston that can move without friction; consequently, the reaction and permeate side volumes change according to the piston movement. In addition, PReaction can be different from PPermeate Side. During the reaction the chamber volumes change in order to achieve the chemical and permeating equilibria. In the plug-flow MR, there are no moving parts as in batch MR, however, permeation changes flow rates of both reaction and permeate streams. Algorithm used for the equilibrium calculation of a MR [12] integrates the method of the reactor in series, already utilised for the calculation of the chemical equilibrium (in TR), with the constrain expressed by the permeating equilibrium, Eq. (1).
3. Results and discussion MSR and WGS reactions have been considered in this work to calculate the MR equilibrium conversion due to their importance in many industrial processes. In particular, MSR is one of the most important industrial processes for H2 [14] and syngas production. The catalytic process involves several elementary reactions, however, a kinetic study of MSR [15] over Ni-based catalysts shows that the reaction rate might consider the following three global reactions: (1) CH4 H2 OCO3H2 (2) COH2 OCO2 H2 (3) CH4 2H2 OCO2 4H2
DH298 206 kJ mol1 DH298 41 kJ mol1 DH298 165 kJ mol1
However, the reaction (3) can be excluded from the thermodynamic analysis because of linear combination of the first two reactions. The WGS reaction (2) is present in many chemical processes, which involve hydrocarbon transformations, e.g., partial oxidation, reforming, etc. The tool developed by Barbieri et al. [12] was used to calculate the equilibrium conversion for a MR when a reaction (e.g. MSR or WGS) occurs. Equilibrium conversion of MSR is an increasing function of T and I (Fig. 3). The increase in the conversion is higher at intermediate T; whilst at a lower T the conversion difference of a MR and a TR decreases because the permeation effect is very low due to low H2 partial pressure in the reaction chamber. At high T (/ 500 8C), the conversion for I /10 is /90%, a further increase in I shifts the equilibrium to a total conversion. The use of a MR is convenient also for the WGS reaction. The conversion is, in this case, a decreasing function of T (Fig. 4); however, it shows a significant increase when I increases. Major advantages were showed at higher T ; at 400 8C the conversion degree
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Fig. 3. CH4 equilibrium conversion vs. T for MSR reaction at different I values. PReaction /PPermeate Side /1 bar, reactant (H2O/ CH4) molar ratio/3.
Fig. 4. CO equilibrium conversion vs. T for WGS reaction at different I values. PReaction /PPermeate Side /1 bar, reactant (H2O/CO) molar ratio/1.
moves from 75% for a TR to about 90% for a MR (I/ 10). MSR reaction is characterised by Dn /0 and thus it is not favoured by pressure, as shown, for a TR, in Fig. 5.
Fig. 5. CH4 equilibrium conversion vs. T for MSR reaction at different reaction pressures. PPermeate Side /1 bar, reactant (H2O/ CH4) molar ratio/3, I/10.
The curves relative to higher pressures are located under the curves corresponding at atmospheric reaction pressure. The situation is completely different for a MR where an increase of the reaction pressure produces an increase in the driving force for the permeation and then a higher equilibrium conversion. The same positive effect is showed by a MR for the WGS reaction (Fig. 6) that is characterised by Dn /0. However, reaction pressure increases the permeation driving force and consequently there is a large advantage in the global performance of the reactor. The pressure has a positive effect on MR equilibrium for any reaction type (Table 2) also for the reaction characterised by Dn /0 such as, e.g. MSR. In addition, the permeation reduces the reaction volume for a batch MR or the outlet reaction stream of a plug-flow MR. In Fig. 7 the CH4 conversion, in the MSR reaction, is reported versus the reaction pressure. The MR conversion is an increasing function of the pressure at higher I; when the reaction temperature and I are lower (0/ 500 8C, I/1) the conversion profile presents a minimum at a lower value (a few bars) of reaction pressure. TR conversion decreases in the whole pressure range. Equilibrium conversion depends on the pressure for two different factors: one negative, due to the reaction pressure, and one positive, due to an increase of the permeation driving force. At 500 8C and I/1 these two effects are comparable, and they generate a minimum. The two opposite effects on the conversion are equal, for a MR at 600 8C with I /1, and the profile presents a flex point. When the permeation is improved increasing I , the flex point disappears. The conversion after the minimum increases monotonically. In a MR, H2 partial pressures on reaction and permeate sides are equal under equilibrium condition. H2 partial pressure shows the same behaviour of the conversion degree increasing for a MR and decreasing for a TR (Fig. 8). In addition, it decreases when I
Fig. 6. CO equilibrium conversion vs. T for WGS reaction at different reaction pressures. PPermeate Side /1 bar, reactant (H2O/CO) molar ratio /1, I/10.
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Table 2 Pressure effect and variation of the reaction volume or the outlet flow rate on reaction side in batch or plug-flow TR and MR Mole number variation
Dn B 0 Dn 0 Dn 0
TR
MR
Pressure effect
Batch / Reaction volume variation
Positive No Negative
Reduction No Expansion
Plug-flow / Reaction stream variation
Pressure effect
Batch / Reaction volume variation
Positive Positive Positive
Reduction Reduction Depend on the reaction
Plug-flow / Reaction stream variation
4. Conclusions
Fig. 7. CH4 equilibrium conversion vs. PReaction for MSR reaction. Reactant (H2O/CH4) molar ratio/3.
Fig. 8. H2 partial pressure under equilibrium condition in the MSR reaction. TReaction /500 8C, PReaction /1 bar, reactant (H2O/CH4) molar ratio/3.
Equilibrium conversion of a Pd-based MR was studied for hydrogenation reactions such as MSR and WGS using a thermodynamic tool based on ‘reactor in series method’. In order to evaluate the MR conversion, the relation of the permeating equilibrium was added, as constrain, to the thermodynamic constants already used to calculate the equilibrium of a TR. The equilibrium conversion increase is related to the extractive capacity of the system represented by the sweep factor. Sweep factor is identified, in addition to those characterising a TR, as a characterising variable for a MR. In fact, equilibrium conversion is an increasing function of I. In order to validate the choice of the sweep factor as characterising variable some simulations (using a mathematical model [12]) were performed changing some parameters, e.g. feed and sweep flow rates, membrane thickness, etc. All simulations showed the same result, the same values of equilibrium conversion, at a set I value. The different effect of the reaction pressure on the equilibrium of MRs and TRs is another interesting thermodynamic result. The conversion of a reaction characterised by no variation of the number of moles, e.g. WGS, in a TR is independent from reaction pressure. On the contrary, the conversion is an increasing function of reaction pressure in a MR. This advantage is more evident for the MSR reaction characterised by an increase in the number of moles: a reaction pressure increase gives, in a MR, a higher equilibrium conversion, when in a TR the effect is a strong reduction of conversion.
Acknowledgements increases, whereas, the CH4 conversion and H2 amount increase. Its increase is higher at lower I : at 500 8C, it passes from about 0.3 bar to about 0.75 bar when I decreases from 10 to 1. An analogous behaviour is showed at 600 8C.
The financial contribution of the INCO-Copernicus project Contract No. IC15-CT98 0512 and MURSTItaly project ‘Nuove membrane per la realizzazione e lo sviluppo di reattori catalitici a membrana*/Cofinanziamento 1999’ are gratefully acknowledged.
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Appendix A: Nomenclature List of acronyms CSTR continuous stirred tank reactor MR membrane reactor MSR methane steam reforming PFR plug flow reactor SCCM cm3 (TPS)/min TR traditional reactor WGS water gas shift List of symbols d membrane thickness (mm) DH reaction enthalpy (kJ/mol) Dnj variation of the mole number in the reaction jth I sweep factor, see Table 1 n mole number P pressure (Pa) T temperature (8C) X CH4 or CO conversion
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